The dual function \(\underset{\mathbf {P}}{\text{max}} \;\mathbb {L}(\mathbf {\Lambda },\mathbf {P})\)  is the pointwise supremum of a family of functions of \(\mathbf {\Lambda }\) , it is convex [1]} and the
globally optimal values for \(\mathbf {\Lambda }\)  can be found by using any of the numerous convex optimization techniques. In this work,we adopt the bisection method. Let \(\underline{\lambda _{i_a}}\)  and \(\overline{\lambda _{i_a}}\) , for \(i_a \in \mathcal {L} \)  or \(i_a \in \mathcal {R} \) , denote the upper and lower bound for the Lagrange multiplier search for node \(i_a\) . Let \([0, \overline{\lambda _{i_a}^{max}}]\)  denote the maximum search interval for the multipliers for node \(i_a\) .
The WSR maximization hybrid beamforming design for the massive MIMO interference channel is given in Algorithm  REF
